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We just finished, hopefully,
getting intuition for why my

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initial pressure times my
initial volume divided by my

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initial temperature is going
to equal-- if I change the

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volume, the pressure, the
temperature, or some

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combination of all of them,
it's going to equal my new

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pressure times my new volume
divided by my new temperature.

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And once again, just remember
all of this-- pressure times

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volume is proportional to the
amount of kinetic energy in

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the system, and temperature is
proportional to the amount of

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kinetic energy per molecule.

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If we don't change the number of
molecules, the amount-- and

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since by the conservation of
energy, the amount of kinetic

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energy isn't going to change
unless we do some work, or get

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some potential energy-- these
quantities and this

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relationship won't change.

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Watch the last video, and
hopefully you'll get some

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intuition-- if it's still
confusing, I'll make another

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video for you guys.

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Before I apply this equation--
this is going to get you

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pretty far in thermodynamics
just knowing this, and even

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more just having the intuition
of what it means.

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I want to clarify something
about temperature-- there's a

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lot of different ways to
measure temperature.

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We know that in Fahrenheit,
what's freezing of water?

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It's 32 degrees Fahrenheit
that's freezing, but that's

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also 0 degrees Celsius--
actually, that's how the

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Celsius scale was determined.

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They said, where does water
freeze, and then where does

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water boil?

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100 degrees for Celsius
is boiling, and that's

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how they rated it.

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You could be colder than the
freezing of water, and you'd

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have to go negative in that
situation-- Fahrenheit, I'm

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actually not sure.

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I need to look that up in
Wikipedia, or that might be

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something for you to do, and
tell me how it came out.

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I think the boiling of water in
Fahrenheit is 212 degrees,

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so it's a little arbitrary.

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I think Fahrenheit might be
somehow related to human body

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temperature, but I'm
just guessing.

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You can have different scales
in this situation, and they

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were all kind of
a bit arbitrary

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when they were designed.

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They were just to have some type
of relative to scale--

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you could say when things are
boiling, they're definitely

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hotter because they have a
higher temperature then when

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things are freezing.

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You can't divide 100 by zero,
but if something is 1 degree,

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is it necessarily the case that
something that is 100

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degrees Celsius is a hundred
times hotter, or has a hundred

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times the kinetic energy?

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Actually, what we'll see is that
no, it's actually not the

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case-- you don't have 100 times
the kinetic energy, so

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this is a bit of an
arbitrary scale.

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The actual interval is
arbitrary-- you could pick the

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1 degree as being one hundredth
of the distance

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between zero and 100, but where
you start-- at least in

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the Celsius scale-- is
a bit arbitrary.

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They picked the freezing
of water.

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Later on, people figured out
that there is an absolute

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point to start at.

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And that absolute point to start
at is the temperature at

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which a molecule or an atom has

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absolutely no kinetic energy.

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Because we said temperature is
equal to the average kinetic

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energy of the system, or the
total kinetic energy of the

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system divided by the
number of molecules.

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Or we could also
say the average

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kinetic energy per molecule.

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The only way to really say that
the temperature is zero--

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and this is proportional,
because the temperature scales

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are still a little bit
arbitrary-- the only way to

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get to a temperature of zero
should be when the kinetic

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energy of each and every
molecule is zero, or the

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average kinetic energy.

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So they're not moving, they're
not vibrating, they're not

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even blinking-- these molecules
are stationary.

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The point at which that occurs
is called absolute zero.

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That actually occurs-- absolute
zero, which is also

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called zero Kelvin, and that is
the same thing as minus 273

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degrees Celsius.

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Nowhere in the universe, at
least that I'm aware of, it is

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it colder than minus 273 degrees
Celsius-- at that

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temperature, nothing moves,
even at the atomic scale.

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I'm talking that the electrons
collapse into the nucleus--

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everything is completely
stationary at zero Kelvin.

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It's a theoretical absolute
limit-- maybe we'll do a bunch

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of videos on how you can get
close to that, but in

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laboratory environments or maybe
in deep space, it gets

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really, really close to this.

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I'm pretty sure nowhere in the
universe do we have absolutely

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zero Kelvin, or at least in any
place where we actually

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have particles, but I might be
wrong there-- that's a little

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bit out of the scope of what
we're talking about.

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The true way to measure
temperature is in Kelvin.

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When you're measuring in Kelvin,
if I say-- I have

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something that is 1 kelvin
versus something that is 5

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kelvin, since we nailed down the
bottom at a point at which

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really do not have kinetic
energy, I can make the

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statement that this has five
times the energy of something

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that's at 5 Kelvin
versus 1 Kelvin.

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That whole long explanation
about Kelvin, that was to just

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to make the point that whenever
we use this formula,

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or really any formula in
thermodynamics that involves

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temperature, we should convert
to Kelvin, unless we're just

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doing change in temperature.

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Then you could you could
probably keep it Celsius, but

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when you're doing
proportionality, or you're

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using it for multiplying or
dividing by temperature, you

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have to use Kelvin.

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Hopefully, I made a little
bit clear of why that is.

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Let's do an example.

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You'd be surprised how
far this takes you.

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Really, the main trick is
just to remember to

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convert things to Kelvin.

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That's the number one reason why
people miss questions on

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thermodynamics exams-- is that
they didn't convert to Kelvin.

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This problem is very typical of
most of what you'll see--

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this is from the Barron's AP
physics B on page 226.

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It says a confined gas is a
temperature of 27 degrees, so

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its initial temperature
is 27 degrees Celsius.

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It has a pressure of 1,000
pascals, or newtons per meter

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squared, and the volume
is 30 meters.

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I think in one of the early
videos, I think I said newtons

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per meter cubed, but it's
newtons per meter squared-- I

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just want to make sure I
didn't confuse people

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previously, so that's
the initial volume.

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It says the volume is decreased,
so then we go to

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this date, where my new
volume is going to

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be 20 meters cubed.

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The new temperature is
increased, and so the new

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temperature is now 50
degrees Celsius.

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They want to know what
is the new pressure?

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Before we just substitute into
the equation, and solve for

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the new pressure, remember--
if they gave it to you in

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Celsius, convert to Kelvin.

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If they gave it to you in
Fahrenheit, which they seldom

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do, then convert into Celsius,
and then convert to Kelvin.

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We already know that zero
Kelvin is equal

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to minus 273 Celsius.

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Or another way you could say it
is x Kelvin is equal to--

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essentially, whatever degree you
get in Celsius, you just

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add 273 to it.

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Does that make sense?

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Think of it this way: if
you're at zero degrees

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Celsius, you're already 273
degrees above zero Kelvin.

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Think about that, and hopefully
that makes sense--

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maybe you want to draw a number
line just to make sure.

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Whatever Celsius degree you
have, just add 273 to it, and

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you'll get Kelvin.

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Add 273 to 27 degrees Celsius,
and that's 300 Kelvin, and

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then 50 degrees Celsius
is-- add 273 to it.

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So 50 plus 273 is 323,
so now we can

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substitute into this formula.

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P1, 1,000 pascals times V1 times
30 divided by the first

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temperature-- remember
to do it in Kelvin--

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300, is equal to P2.

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We don't know what that is.

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P2 times V2 times 20 divided by
our new temperature, 323.

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We can simplify this: we could
take two 0's off of here, take

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two 0's off of here, then you
could take a 3 out of here,

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and then take a 3 out of here,
and we're left with 100.

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This is equal to 100-- that was
30,000 divided by 300, and

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so that's 100 on the
left-hand side.

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So we have 100 is equal to
P times 20 over 323.

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I'm running out of time.

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If I were to solve for it, 323
times 100 divided by 20

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equals-- so my new pressure
is 1,615 pascals.

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I just solved this equation,
and the hard part was

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converting to Kelvin.

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See you in the next video.

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